The Wronskian 1. Show that the functions e", cos x and sin x are linearly independent. 2. Show that 1, sin? x and cos? x are linearly dependent.

Q: 4. Find two possible non-linear functions & and such that goh= √sinx-x²

A: To find the non linear function by the given composition.

Q: 2. Find an interval where f,(x) = sin2 x and f2(x) = cos² x are linearly independent. %3D

A: W(π/4) = -sin(π/2) = -1 W(π/6) = -sin(π/3) = - √3/2 Since, Wronskian is not zero for a single value…

Q: 5. Find the values of a and b such that dx tan 1 + sinx a + b . %3D

A: We need to integrate ∫11+sinxdx

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A: To find value of a, b, c we need to draw the  graph of function then measure the value. Note that…

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A: Using definition of composite function.

Q: 4. Evaluate tan (4.3 – j1.1).

A: Given that, evaluate tan (4.3 - j1.1).

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A: We have to proof that given relation

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Q: dz (2) Suppose z is a function of x and and suppose cos(32) xyz?. Find in Y, terms of x, y, and z.

A: The given function is, cos3z=xyz2

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Q: Q57.a) Find if y=sin(tant) and t=cos(x) dx

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Q: Evaluate dx 9. x2 |1 4x2

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A: Find the Maclaurin expansion of  f(t)= cost

Q: Prove that i2-i0 e-e %3D sincd

A: We have to prove eiθ-e-iθsin θ=2i Now, sin x can be expressed in exponential form as sin…

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A: We have, sinx=x-1 Let us consider a function fx such that, fx=x-1-sinx

Q: Q if asinx Prove that a + bcos X y' = (a+ bcosx)? a cos+ b

A: Differentiate wrt x In problem, proof equation is wrong I have solved properly

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A: Since we only answer up to 3 sub-parts, we'll answer the first 3. Please resubmit the question and…

Q: 17. If 2 tana tan?ß tan?y + tan a tan-ß + tan B tany + tan?a tan?y 1 (a. B.y e R. a. B.y (2x+1)…

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Q: Let y = sinx, if y(n) = sin x then n =

A: This question can be solved using the concept of higher order derivatives.

Q: Find dx 11 for y = 9x2 sin x + 18x cos x – 18 sin x. dx

A: Finding the derivative of y